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Question

Physics Question on physical world

In a new system of units called star units, 1kg=10kg1\,kg^* = 10 \,kg , 1m=1km1 \,m^* =1 \,km and 1s=11s^* = 1 minute, what will be the value of 1J1J in the new system ?

A

2.4×108J2.4 \times 10^{-8}\, J^*

B

3.6×104J3.6 \times 10^{-4}\, J^*

C

4.2×103J4.2 \times 10^{-3}\, J^*

D

4.2×102J4.2 \times 10^{-2}\, J^*

Answer

3.6×104J3.6 \times 10^{-4}\, J^*

Explanation

Solution

Given that
For star units 1kg=10kg1kg^* =10\, kg
1m=1km1m^* = 1 \,km
and 1s=1m1s^* = 1 \,m
The value of 1J1 \,J in star units
1J=1[ML2T2]=1[1kgm2s2]1 \,J = 1 [ML^2 T^{-2}] = 1 [1\, kg\,m^2s^{-2}]
=[1×110kg+(m1000)2+(s60)1]= \left[1\times \frac{1}{10} kg + \left(\frac{m^*}{1000}\right)^{2} + \left(\frac{s^*}{60}\right)^{-1}\right]
=3.6×154J= 3.6 \times 154 J